I have Symantec Client Antivirus on my Computer at work, and I can't accsess the web, How can I update the antivirus Program?without buying a new Software?

You have to get a new subscription to be able to update properly. If this is at work ask the Administrator what's up with not having up to date Antivirus. They may just update for you on the server. Can't imagine them not updating this for a company computer. Just because you can't access the web to update they probably do it automatically.

If the computer is not on the web (can't access the web) then is there really a risk or a virus on a computer not linked to the web ?

Could you get temp access to web to update